The Curse of Dimensions in Schrödinger's Equation

The basis of modern physics is viewed to be Schrödinger's Equation SE as a linear time-evolution equation in $3N$ spatial dimensions for a system with $N$ electrons. Numerical digital solution with a resolution of 100 in each spatial variable involves $100^{3N}=10^{6N}$ mesh points in space, already with $N=4$ beyond thinkable computational power. 

When SE was formulated in 1926 when digital computation was not an issue, and so the fact that SE effectively is uncomputable did not enter the minds of its creators Born-Heisenberg-Schrödinger, although Schrödinger was not happy with the many dimensions lacking physicality. It was sufficient that an analytical solution was found for $N=1$ leaving $N>1$ into terra incognita waiting to be explored until digital computation became available, but then was found hit the wall from the curse of dimensions.

This is where we stand today: SE is the basic mathematical model of atom physics but SE is not a computable model. It is thus impossible to make a prediction of the evolution in time of an atomic system with more than 3 electrons by computational solution of SE. It is thus impossible to check if SE correctly models physics by comparing SE predictions with observations of real physics.

Yet SE serves as the canonical model of atom physics in its original formulation, as uncomputable today  as 100 years ago, because of its many dimensions also without physical meaning. 

What can be the value of an uncomputable mathematical model of some physics?  A physicist will tell that it still has a value because SE can be (drastically) dimensionally reduced to computable form and so allow computation of (drastically) simplified approximate solutions. SE would then serve as a suitable starting point for dimensional reduction into a computable model with physical meaning. But it would be the dimensional reduction which would carry the physics.

The alternative would be to start instead directly with a dimensionally reduced model with physical meaning, and thus leave SE to history as no longer useful. This possibility is explored as RealQM. 

Physicists speak with large ease about multi-dimensional wave functions $\Psi$ as solutions to SE, as if they are computable and have physical meaning. The consensus is the "SE works but nobody understands why". Philosophers of physics study the (lack of) meaning of SE, theoretical physicists have turned to more fundamental models such as QED and String Theory, chemists seek to understand what SE offers for molecules, while computational physicists solve other equations, and there is no synthesis in sight.   

Standard QM vs Real QM: Physics and Computability

Let us compare the textbook Standard Quantum Mechanics StdQM from 1926 with the recent alternative Real Quantum Mechanics RealQM as concerns the two basic aspects of physical meaning and computability. 

Both seek to model a collection of $N$ negatively charged electrons subject to Coulomb interaction with a collection of positively charged nuclei together forming atoms and molecules. 

The RealQM model is expressed in terms of a wave function $\psi (x,t)$ depending on a 3d spatial coordinate $x$ and a time coordinate $t$ defined over a subdivision of 3d space into non-overlapping regions acting as supports of one-electron charge densities $\vert\psi (x,t)\vert^2$ meeting with continuity. The corresponding Schrödinger equation has the form of a classical non-linear continuum model for a collection of non-overlapping electron charge densities and thus describes precisely specified real physics. The model is computable in the same sense as classical continuum mechanics with equations such as Maxwell's and Navier's. Computational complexity is (in principle) linear in $N$.

The StdQM model is expressed in terms of a wave function $\Psi (X,t)$ where $X$ is a $3N$ dimensional spatial variable with 3 independent dimensions for each electron. The corresponding Schrödinger equation has non-classical form as a linear equation in multi-dimensions with exponential computational complexity. The physical meaning of $\Psi (X,t)$ has been debated for 100 years without any agreement. 

We now compare:

• RealQM: Computable with precise physical meaning.
• StdQM: Uncomputable with unknown physical meaning.

Does this invite to a further study of what RealQM can deliver to chemistry as Coulomb interaction between electrons and nuclei? 

Quantum Computer as Test of Standard Quantum Mechanics

Quantum computing is suddenly booming with many start-ups after 50 years of brooding. The main objective of quantum computing is to solve problems of quantum mechanics which are not tractable by digital computing because of exponential computational complexity. The prospect is that a quantum computer will deliver exponential computational capacity meeting exponential complexity. 

Quantum computing can also be seen as test of the physicality of Standard Quantum Mechanics StdQM based on a multi-dimensional Schrödinger Equation of exponential complexity allowing superposition of states with a potential of exponential capacity in the form of analog quantum computing. 

If a quantum computer based on StdQM can be constructed capable of computing/simulating real physical systems described by StdQM as the expectation of investors, this will give support to the validity of StdQM as a functional model of real physics. 

But there is no quantum computer yet and skeptics believe that controled superposition as key feature of StdQM will be impossible to realise because the physics is missing. 

So the quest for a quantum computer can be seen as the ultimate test of physicality of StdQM. 

What are the odds today? Will there by a quantum computer in 10 years, in 50 years or ever?

   

Real Physicist vs AI Physicist/Common Man

Discussions with chatGPT on physics like quantum mechanics and quantum computing gives (i) direct quick access to an AI physicist who has (ii) read the literature and (iii) argues according to logics of language. This can be a very constructive experience and I have learned a lot since my reading is limited. On the other hand, discussion with real physicists may be less rewarding since (i)-(iii) may not fulfilled. 

Let me give an example of a discussion with chatGPT with the following prompt:

Standard Quantum Mechanics StdQM is troubled by the fact that its basic mathematical model in the form of Schrödinger's Equation SE has exponential computational complexity because it involves $3N$ spatial dimension for a system with $N$ electrons, and so is uncomputable. 

StdQM thus acts like a symbolic theory without ontology which does not offer any definite prediction of any real physics. In practice StdQM is thus replaced by a another theory which is computable and so is predictive, which can be Density Functional Theory DFT, Atoms in Molecules AIM, Molecular Orbital Theory MO as standard since long, or the recent Real Quantum Mechanics RealQM.

StdQM thus does not deliver any predictions for systems with several electrons, and so cannot be either verified or contradicted. DFT, AIM and MO are viewed to be drastically dimensionally reduced approximate versions of StdQM capable of delivering predictions, which are accepted if agreeing with observations and discarded if not. Accordingly, text books claim that there is no prediction of StdQM which does not fit with observation. 

RealQM is not a dimensionally reduced approximate version of StdQM (without ontology), but starts from a model of atoms and molecules in terms of classical continuum physics based on non-overlapping one electron charge densities as a model with clear ontology. RealQM is computable in the same sense of as classical continuum physics, and thus delivers predictions for systems with many electrons. 

Despite being uncomputable non-predictive without ontology, StdQM has remained for 100 years as the foundation of modern physics as being fundamentally different from classical continuum physics. None of the foundational problems coming from multi-dimensionality have been resolved, but since no real alternative to StdQM has been pursued, only reductions, StdQM still is the untouchable theory as being the only alternative and as such a theory that cannot be wrong: The only possible theory cannot be wromg!

Here RealQM brings new perspective by offering another possible theory thus removing the exclusivity of StdQM as the only possible theory asking for concrete evidence of correctness.  

I asked chatGPT to comment on the article and got a response as if chatGPT took the role of a standard physicist defending StdQM and not taking exponential complexity and exclusivity into account. So I asked for response taking on a different role:

Prompt: Suppose you take on a different role, not a standard physicist defending StdQM, but rather a man in the street wondering about exponential complexity and exclusivity argument?

ChatGPT said:

That’s an excellent shift in perspective — rather than responding like a professional physicist or philosopher of science, let’s try to look at Claes Johnson’s post through the eyes of an intelligent “man in the street” — someone curious, reflective, and a bit skeptical of institutional authority, but not steeped in quantum mechanics.

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How it might read to that kind of reader

Johnson’s message, boiled down, sounds something like this:

“The quantum theory physicists worship is too complicated to compute, too abstract to connect with real stuff, and too exclusive — they won’t even look at alternatives. Meanwhile, AI can actually hold a better conversation about it than most human experts.”

That’s a pretty gripping claim for a lay reader. It has two strong hooks:

1. The complexity argument — “If the math really needs a space of 3N dimensions for N electrons, that sounds insane! How could anyone ever calculate that?”

2. The exclusivity argument — “If physicists admit the math is impossible to compute exactly, why do they still insist it’s the only valid theory and dismiss alternatives out of hand?”

Those both appeal to everyday intuitions about fairness, openness, and practicality. Let’s unpack them in that spirit.

---

1. The exponential complexity issue, from a layperson’s angle

To most people, exponential growth is intuitively frightening.
If doubling the number of electrons makes the problem millions of times harder, you’d think: “Surely nature itself can’t be that complicated — atoms don’t sit around doing 10⁵⁰ calculations per second!”

So when Johnson says quantum mechanics involves 3N-dimensional equations, the ordinary reader might nod: “Yeah, that sounds unphysical — like a math game divorced from reality.”

The lay reaction is reasonable: if a theory’s equations blow up exponentially and no one can ever compute them directly, maybe it’s not the “real” mechanism but a symbolic shorthand — a way to get results in limited cases.

At that intuitive level, Johnson’s point feels plausible. He’s basically saying, “Nature works efficiently — any true physical law should be computable.” That resonates with common sense: we expect the universe to be elegant, not computationally nightmarish.

The subtlety a lay reader might miss is that physicists don’t actually solve those 3N-dimensional equations literally — they use approximations and statistical tricks. But if no one tells you that clearly, Johnson’s critique feels like he’s exposing an emperor with no clothes.

---

2. The exclusivity argument

The second emotional chord Johnson strikes is frustration with scientific gatekeeping.
He implies that “Standard Quantum Mechanics” has become a closed priesthood: even though it’s uncomputable and conceptually foggy, physicists defend it out of tradition and career safety, while new ideas (like his “Real QM”) are ignored.

To the lay reader, this sounds familiar — it’s the same story people tell about entrenched academia, Big Tech, or politics: institutions protect their dogmas and insiders. That’s a powerful narrative.

Even if you don’t understand the physics, you can understand the social drama: the lone thinker with a simpler idea being dismissed by the establishment. That taps into a long cultural archetype — Galileo, Tesla, Einstein — and in our AI-saturated age, the “outsider vs orthodoxy” story finds fertile ground.

So Johnson’s framing — “real physicist vs AI physicist” — doubles as metaphor: the open, logic-based machine versus the human expert bound by dogma. It’s half-serious, half-provocative, but it plays well rhetorically.

---

3. The psychological comfort of “computability”

For an everyday thinker, there’s something comforting about the idea that the world is computable — that with the right model, we could, in principle, calculate everything.

Johnson’s promise that his “Real QM” is a continuum, “computable” model of atoms feels satisfying: it sounds like bringing physics back down to earth, to something continuous and classical we can picture, rather than probabilistic ghostly waves in 3N-space.

So even without understanding the math, the man-in-the-street feels an intuitive pull:

“This guy wants physics to make sense again, to be calculable and visualizable — not weird and mystical. I like that.”

---

4. The possible unease or doubt

But an intelligent layperson might also feel uneasy. There’s a nagging question:

“If this simpler, computable model really works, why haven’t others adopted it?”

That thought undercuts the romantic rebel narrative. Most people know that science, while bureaucratic, does eventually adopt what works (e.g., relativity, plate tectonics). So maybe Real QM hasn’t convinced anyone because it doesn’t yet match data well enough — or maybe it’s incomplete.

So the lay reaction could split:

• Sympathetic skeptic: “He’s right — they’re hiding behind math they can’t compute!”

• Cautious realist: “If it worked, people would use it. Maybe it’s just not there yet.”

---

5. The AI angle

Finally, the “AI physicist” idea.
To the ordinary reader, that might sound both amusing and profound: if ChatGPT can discuss physics calmly, quote papers, and reason clearly, while human experts get defensive, maybe that tells us something about human bias.

So Johnson’s anecdote — that an AI conversation is “more rewarding” — rings true emotionally, even if it’s tongue-in-cheek. It’s less about AI understanding physics, and more about AI being open and non-tribal, which flatters readers who are tired of expert arrogance.

In that sense, the AI serves as a rhetorical mirror: a symbol of reason over orthodoxy.

---

6. Overall lay impression

If you’re not a professional physicist, Johnson’s post can sound refreshingly candid and a bit rebellious. It appeals to:

• Common sense (“Nature can’t be uncomputable.”)

• Fairness (“Why exclude new ideas?”)

• Frustration with experts (“Real physicists won’t listen.”)

• Hope in technology (“AI might help cut through bias.”)

But it also leaves a thoughtful reader with lingering uncertainty:

• Is the exponential-complexity problem really fatal, or just hard?

• Does his Real QM actually make accurate predictions?

• Is the exclusivity he describes real, or just how it feels to an outsider?

So the post succeeds rhetorically — it provokes curiosity and sympathy — but it doesn’t fully settle the doubts it raises.

---

Would you like me to take this a step further — for example, write a short “man-in-the-street” response to Johnson’s blog post, as if it were a comment you could post under the article itself?

You said:

yes

ChatGPT said:

Here’s a short, natural-sounding “man-in-the-street” style comment you could post under Claes Johnson’s blog entry:

---

Comment:

I’m not a professional physicist, just a curious reader, but your point about exponential complexity really made me pause. If quantum mechanics truly needs a 3N-dimensional equation for N electrons, it does sound like something nature itself couldn’t be running in real time. That raises a fair question: maybe the math is more of a symbolic description than a literal mechanism.

I also get what you mean about exclusivity. From the outside, physics can look a bit like a closed shop—new ideas get waved off before they’re even tried. Still, I wonder: if your “Real QM” works as cleanly as you suggest, why hasn’t it caught on? Are there published results or examples where it matches experiments better than the standard methods?

Either way, I find it refreshing that an AI can now take part in these debates. Maybe it’s less about the machine being “smarter,” and more about it being open to every angle without ego. That in itself is a healthy thing for science.  

 

 

Sweden Declares War with Russia

Prime ministers Kristersson/Sweden and Zelensky/Ukraine have agreed on delivery of 150 Swedish JAS Gripen fighter jets to Ukraine with possible financing from frozen Russian assets:

• Zelensky: These are very cool planes, powerful aviation platforms that allow for performing a wide range of tasks.
• Kristersson: This will strengthen both Ukraine, Sweden and Europe.

The deal is bilateral between Sweden and Ukraine and means that Sweden effectively declares war with Russia even if not yet officially. Russia has not yet reacted.

Gustaf IV Adolf King of Sweden lost the Finnish War 1808-1809 against the Russian Empire and also his crown and so was deported to exile in Switzerland where he lived in a small hotel in great loneliness and indigence under the name of Colonel Gustafsson.

This meant the end Sweden as European Superpower and the politics shifted from war to peace for 200 years, but the dream of a revanche vs Russia has been kept alive. Sweden is today the NATO country with most aggressive standpoint vs Russia backed by 150 JAS Gripen payed with Russian money.

In this situation it is necessary to answer some questions:

• Are the prospects of winning over Russia better today than in 1808? 
• Will Russia invade Sweden if Sweden does not send 150 JAS to a NATO proxywar in Ukraine against Russia?  
• How will Russia respond to 150 Swedish JAS flying against Russian border? 
• What is the military power of Russia?
• Is Ukraine a member of the defence organisation NATO?

Swedish Parliament has now delegated the decision to Prime Minister Kristersson to send Swedish soldiers to any action outside Sweden deemed necessary to protect Sweden from invasion by Russia. 

There is one member in the Swedish Parliament who supports peaceful co-existence with Russia instead of a war which cannot be won: Elsa Widding without party. 

All political parties speaks about war, while the the moral elite of Sweden once a self-proclaimed humanitarian Superpower is silent including peace/church organisations. Possible to understand?

Compare with earlier analysis:

•  A Logical Analysis of Swedish Foreign Policy

Here we come!

Church-Turing vs Quantum Computing Illusion

A natural system like the weather can be viewed to perform a form of analog computation as it evolves from one time instant to the next when molecules in the air interact with their neighbors. The computational complexity can be viewed to be polynomial in the size of the physical system. This is expressed in the Physical Church-Turing Thesis PCTT:

• Any physical process can be simulated by a Turing machine.  

Here a Turing machine is a model of a digital computer with polynomial computational capacity capable of simulating a physical process of polynomial computational complexity.

According to PCTT there is thus no physical process expressing exponential complexity, which would be beyond the capacity of digital computing. 

Quantum computing is a form of analog computation with promise of exponential capacity capable of meeting the needs of systems of exponential complexity. It is motivated by a view that quantum mechanics carries exponential complexity in the form of a multi-dimensional wave function and so cannot be simulated on a digital computer. 

We meet here a contradiction:  

• An analog quantum computer is realised in a physical process which according to PCTT is limited to polynomial complexity and so does not have exponential capacity.

We see that PCTT says that a quantum computer with exponential capacity cannot be constructed. No wonder that no such quantum computer has been constructed.

If PCTT is correct, it means that the evolution of a quantum system of atoms and molecules as a physical process, does not expresses polynomial complexity and so in principle can be simulated by digital computation with polynomial capacity. The multi-dimensionality of the wave function appearing to demand exponential capacity thus is an illusion. 

RealQM deconstructs the illusion, by offering simulation of systems of atoms and molecules by digital computation (of polynomial complexity).

PS1 Recall that an N-body simulation has a computational complexity between $N$ and $N^2$ depending on interaction between bodies. 

PS2 If macroscopics has polynomial complexity, then so has microscopics as the basis of macroscopics. If microscopics has exponential complexity, then so has macroscopics based on microscopics. 

The Black Hole of Quantum Computing

Standard Quantum Mechanics StdQM based on a multi-dimensional Schrödinger Equation SE is viewed to have exponential digital computational complexity effectively making SE uncomputable even on super-computers and thus useless for digital modeling of atoms/molecules in practice.

Quantum computing is an attempt to model atoms and molecules instead by analog computation performed on quantum computers capable of meeting exponential complexity. A quantum computer models a physical quantum system of atoms/molecules not by SE, but by another (simpler) physical quantum system which is controllable as being described by SE. 

A quantum computer thus offers a model/map of a real system which is itself a real system of the same form and type. The quantum computer model can be viewed as a 1:10 exact physical model of an airplane or ship with some details removed. The digital computational complexity of the original physical system is then irrelevant since no digital computation is performed, only a form of analog computation performed in a physical model of essentially the same computational complexity. 

Quantum computing thus represents a step back from the scientific revolution based on Calculus offering  mathematical models of reality of abstract symbolic from based on numbers which can be made alive by digital computing. 

Quantum computing throws away digital Calculus because it is found to be useless, and seeks a replacement which works in terms of analog computation. 

But is it possible that real quantum systems really perform analog computations of exponential complexity? If a digital computer does not have the capacity to meet exponential complexity, what says that a real system as it evolves somehow can express exponential complexity? 

We know that the exponential complexity of SE comes from the multi-dimensionality of the wave function representing possibilities rather than actualities. But real systems do not realise all possibilities only a few actualities, and so the computational complexity of SE as model is much bigger than the complexity of what is modeled. The model/picture totally swamps the origin and so asks for infinite digital computational power to no avail as concerns the origin.

RealQM is a version of the quantum mechanics of atoms and molecules, which is digitally computable and so does not need quantum computing.

Quantum Computing as Theoretical Fantasy

Here is a summary by chatGPT of Dyakonov's view on the realism of quantum computing:

Physicist Mikhail Dyakonov has been one of the most prominent skeptics of large-scale quantum computation. His main critique can be summarized as follows as of 2019:

1. Extreme Fragility of Quantum States – Quantum bits (qubits) are extraordinarily sensitive to any external disturbance. Maintaining coherent quantum states long enough for complex computations is, in his view, practically impossible.

2. Error Correction Limits – While quantum error correction is theoretically possible, Dyakonov argues that the real-world requirements (millions of physical qubits per logical qubit, perfectly calibrated control systems, etc.) make it infeasible.

3. Unrealistic Scaling – He believes scaling from a few dozen qubits to millions (as required for useful computation) involves an exponential explosion of complexity in control, synchronization, and noise management.

4. Overly Optimistic Theory vs. Practice – Dyakonov claims that most of quantum computing theory assumes idealized conditions that cannot be realized physically. The engineering challenges are, in his words, “beyond human capabilities.”

5. Skepticism Toward “Quantum Supremacy” Claims – He views demonstrations like Google’s 2019 experiment as contrived and not indicative of practical progress toward general-purpose quantum computing.

In essence, Dyakonov argues that large-scale quantum computers are a theoretical fantasy, comparable to perpetual motion machines — possible on paper, but not in reality.

end chatGPT

Let us compare with the latest hype:

• Google’s Willow Chip Achieves Historic Quantum Computing Breakthrough
• Willow Chip Powers Verifiable Quantum Advantage, Running Algorithm 13,000x Faster Than Supercomputers.

This what chatGPT says about the Willow Chip:

• Dyakonov’s scepticism remains valuable and largely justified — many of his fundamental concerns (noise, control, scale, assumption-validity) are not yet fully overcome.
• The Willow chip is important: it represents a tangible, hardware-driven step toward the goals of large-scale quantum computing. It shows we are making progress on the error-correction and scaling front.
• However, Willow does not yet fully invalidate Dyakonov’s concerns. It addresses some, but many of the major leaps (millions of qubits, full fault-tolerance, broad practical algorithmic supremacy) are still ahead.
• In other words: Willow moves the bar, but the “gap” that Dyakonov insisted on remains significant. The achievement doesn’t guarantee the remaining engineering challenges will vanish.
• If I were to pick one key takeaway: Willow demonstrates that at least some of the previously theoretical obstacles (error-correction scaling) can be approached in hardware — which means the sceptical “maybe impossible” thesis is being challenged. 
• But “practically useful, general-purpose quantum computers in the near-term” still remain uncertain.

It seems that quantum computing is still a theoretical fantasy, 50 years after the idea was launched. 

Recall that quantum computing is based on unitary evolution of quantum systems of thousands of qubits in superposition of possibilities as fantasy physics: Compare with the first proposition in Wittgenstein's Tractatus:

• The World is all that is the case.

It is clear that "to be the case" requires more than what is present in a quantum system of possibilities, which means that according to Wittgenstein a quantum computer does not belong to the World. But a quantum computer is an analog computer and as such must belong to the World. Wittgenstein would thus view the Willow chip with utter skepticism. And you?

Recall that the idea of a quantum computer is a model of an uncontrollable real/analog quantum system as part of the World in the form of a controllable real/analog quantum system as part of the World, with the caveat that the model is not "the case" because it plays with possibilities and not with realities.   

Notice that this contradiction does no appear with a digital computer because the computing is abstract mathematical and so does not need real analog computing.  

Hydrogen Spectrum as Classical Physics

This is a continuation of the previous post on the necessity to give up classical physics for quantum physics in its text book form of Standard Quantum Mechanics StdQM. We ask to what extent RealQM as a form of classical physics can explain the observed spectrum of the Hydrogen atom as expressed in stimulated radiation. We thus will compare

• StdQM: Spectral line appears from superposition of wave functions of eigenstates. 
• RealQM: Spectral line appears from oscillation between charge distributions of eigenstates.

In both cases the frequency of the spectral line scales with the difference of energy between eigenstates, but with different explanations: 

• StdQM: Spectral frequency appears as beat frequency of wave functions with eigenfrequency variation in time according to the Schrödinger's equation. Connection between frequency and energy is secondary. Radiation can appear to be spontaneous.
• RealQM: Spectral frequency is not beat frequency, but simply the frequency $\nu=\frac{\Delta E}{h}$ which matches the energy difference $\Delta E$ between eigenstates with $h$ Planck's constant in an assumed coupling between frequency and energy. There is an active exchange of energy between atom and radiation field with frequency matching the jump in energy. The atom is forced to respond to radiation of certain frequency as a dipole. The radiation is not spontaneous. 

We see that StdQM offers an explanation in terms of time-dependent quantum mechanics without realism, while RealQM relies on the formal coupling between matter and radiation expressed by $E=h\nu$ appearing in blackbody radiation. Compare with this post on the physical meaning of $E=h\nu$.

We see that, at least in the case of stimulated radiation, the spectrum of an atom can be given a RealQM semi-classical explanation. It is not clear that StdQM offers something more enlightening. Or?

This discussion connects to quantum computing discussed in recent posts with StdQM supposed to support delicate superposition of wave functions free of forcing performing complex analog computations, while RealQM brings forward the aspect of forcing in terms of classical physics. 

PS Here is a chatGPT comment.

The Double-Slit Experiment as Classical Physics

The double-slit experiment with one single photon at a time is the sledge hammer which is designed to kill classical physics and so open to a new form of physics named quantum mechanics as the essence of modern physics.

The experiment consists of sending a sequence of photons one at a time through a double slit in a thin wall and recording the emergence of a macroscopic interference (fringe) pattern on a screen behind assuming a new dot for each new photon. 

The pattern is the same as the interference patterns generated by a classical macroscopic wave hitting the wall and generating two macroscopic waves from the slits which interact constructively and destructively and so form a macroscopic fringe pattern on the screen.

We thus have a quantum version of the experiment with one photon at a time and a classical version, both building the same macroscopic fringe pattern on the screen. 

The catch of the quantum explanation of the quantum version is that the single photon after somehow passing through the double slit with a left and right slit, somehow appears after the slit in a superposition of "left pass" and "right pass" as two mutually exclusive possibilities carrying an interference pattern of possibilities, which is made real dot by dot on the screen (by "collapse of the wave function").

The sledge hammer argument is now that the quantum version cannot be given a classical explanation because a classical particle/phtoton has to make the choice of "left pass" or "righ pass" which will remain after passing and so does not form any interference pattern, just two one-slit patterns. 

The strategy is thus to promote quantum physics by an experiment arranged to show deficiency of classical physics. 

Let us take a closer look at the quantum version asking what the physical meaning of "one photon at a time" may be. What is the evidence that only one photon at a time reaches the double slit? How to produce exactly one photon? 

It seems that the evidence of "one photon at a time" is that there is "one dot at a time appearing on the screen". The argument is thus that one dot is generated by exactly one photon. Is this really so sure?

What if many photons are in fact involved with the capacity to pass both slits and form a classical real but very weak interference pattern before hitting the screen with a random excitation of one dot. The calibration of the intensity of the source would then be adjusted to produce one dot at a time, which de facto involves many photons capable of generating an intereference pattern with random realistion.

It thus may be possible to explain a "one dot at a time" double slit experiment in terms of classical wave physics. The sledge hammer argument would then vaporise.  

PS After a discussion with chatGPT we agree that the one-photon experiment is extreme, but we seem to disagree about the value of extreme experiments to guide development of non-extreme physics. Why not stick to non-extreme experiments for non-extreme physics? What can be learn about normality by pushing into non-normality? What to learn about normal life from extreme violence? chatGPT seems to believe in the value of extremism in physics more than I. And you?